Abstract
Verification bias is a well-known problem that may occur in the evaluation of predictive ability of diagnostic tests. When a binary disease status is considered, various solutions can be found in the literature to correct inference based on usual measures of test accuracy, such as the receiver operating characteristic (ROC) curve or the area underneath. Evaluation of the predictive ability of continuous diagnostic tests in the presence of verification bias for a three-class disease status is here discussed. In particular, several verification bias-corrected estimators of the ROC surface and of the volume underneath are proposed. Consistency and asymptotic normality of the proposed estimators are established and their finite sample behavior is investigated by means of Monte Carlo simulation studies. Two illustrations are also given.
Highlights
Before applying a diagnostic test in clinical settings, a rigorous statistical assessment of its performance in discriminating the disease status from the nondisease status is necessary
At a fixed cut point c, the accuracy of the test can be evaluated by its true positive rate (TPR) and its true negative rate (TNR), which are defined as the probabilities that the test correctly identifies the diseaded and non-diseaded subjects, respectively
This paper proposed several verification bias-corrected estimators of the receiver operating characteristic (ROC) surface of a continuous diagnostic test
Summary
Before applying a diagnostic test in clinical settings, a rigorous statistical assessment of its performance in discriminating the disease status from the nondisease status is necessary. The disease status often involves more than two categories; for example, Alzheimer’s dementia can be classified into three categories (see Chi and Zhou [4] for more details) In such situations, quantities used to evaluate the accuracy of a diagnostic test are the true class fractions (TCF’s). In a three–class diagnostic problem, given a pair of cut points (c1, c2), with c1 < c2, subjects are classified into class 1 if T < c1; class 2 if c1 ≤ T < c2; and class 3 otherwise This implies that the disease classes are ordered with respect to the test result, a condition often referred to as monotone ordering. The authors proposed maximum likelihood estimates for ROC surface and VUS These results only concern ordinal diagnostic tests.
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